Question

A conducting wire is in the shape of a regular hexagon, which is inscribed inside an imaginary circle of radius R as shown in the figure. A current I flows through the wire. The magnitude of the magnetic field at the centre of the circle is

• A. $\frac{\sqrt{3}{\mu }_{0}I}{2\pi R}$
• B. $\frac{{\mu }_{0}I}{2\sqrt{3}\pi R}$
• C. $\frac{\sqrt{3}{\mu }_{0}I}{\pi R}$
• D. $\frac{3{\mu }_{0}I}{2\pi R}$

Answer 1

The correct option is C $\frac{\sqrt{3}{\mu }_{0}I}{\pi R}$

$B=6\left[\frac{{\mu }_0}{4\pi }\left(\frac{i}{Rcos{30}^{\circ }}\right)\right(sin{30}^{\circ }+sin{30}^{\circ }\left)\right]$
$=\frac{\sqrt{3}{\mu }_{0}i}{\pi R}$